Production function, Cost Function for a company

You manage a plant the mass produces engines by teams of workers using assembly machines. The technology is summarized by the production:

q = 5KL

Where q is the number of engines per week, K is the number of assembly machines and L is the number of labor teams. Each assembly machine rents for r = 10,000$ per week and each team costs w = 5,000$ per week. Engine costs are given by the cost of labor teams and machines, plus 2,000$ per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design at the current moment (short run).

a) What is the short run production function?
b) What is the total cost function for your plant to produce q engines (in terms of q only)?
c) What are average and marginal costs for producing q engines in the short run?
d) How many teams are required to produce 250 engines? What is the average cost per engine at this output?

Solution Preview

a) What is the short run production function?

In a short run production function either K or L is fixed. Since you are told that your capital if fixed, your short run production function in this case is q = 25L.

b) What is the total cost function for your plant to produce q engines (in terms of q ...